981 research outputs found
On p.p.-rings which are reduced
Denote the 2Ă—2 upper triangular matrix rings over
ℤ
and ℤp by UTM2(ℤ)
and
UTM2(ℤp), respectively. We prove that if a ring
R is a p.p.-ring, then R is reduced if and only if R does
not contain any subrings isomorphic to UTM2(ℤ) or
UTM2(ℤp). Other conditions for a p.p.-ring to be
reduced are also given. Our results strengthen and extend the
results of Fraser and Nicholson on r.p.p.-rings
Compact Primitive Semigroups Having (CEP)
Abstract Compact completely simple semigroups having congruence extension property (in brevity (CEP)) were first studied by Dumesnil in 1997. In this paper, we study the compact primitive semigroups having (CEP) and characterize such semigroups, so that the result of Dumesnil on compact completely simple semigroups having (CEP) is extended to compact primitive semigroups
An optical fiber network oracle for NP-complete problems
The modern information society is enabled by photonic fiber networks characterized by huge coverage and great complexity and ranging in size from transcontinental submarine telecommunication cables to fiber to the home and local segments. This world-wide network has yet to match the complexity of the human brain, which contains a hundred billion neurons, each with thousands of synaptic connections on average. However, it already exceeds the complexity of brains from primitive organisms, i.e., the honey bee, which has a brain containing approximately one million neurons. In this study, we present a discussion of the computing potential of optical networks as information carriers. Using a simple fiber network, we provide a proof-of-principle demonstration that this network can be treated as an optical oracle for the Hamiltonian path problem, the famous mathematical complexity problem of finding whether a set of towns can be travelled via a path in which each town is visited only once. Pronouncement of a Hamiltonian path is achieved by monitoring the delay of an optical pulse that interrogates the network, and this delay will be equal to the sum of the travel times needed to visit all of the nodes (towns). We argue that the optical oracle could solve this NP-complete problem hundreds of times faster than brute-force computing. Additionally, we discuss secure communication applications for the optical oracle and propose possible implementation in silicon photonics and plasmonic networks.Peer Reviewe
Scaffolding School Pupils’ Scientific Argumentation with Evidence-Based Dialogue Maps
This chapter reports pilot work investigating the potential of Evidence-based Dialogue Mapping to scaffold young teenagers’ scientific argumentation. Our research objective is to better understand pupils’ usage of dialogue maps created in Compendium to write scientific ex-planations. The participants were 20 pupils, 12-13 years old, in a summer science course for “gifted and talented” children in the UK. Through qualitative analysis of three case studies, we investigate the value of dialogue mapping as a mediating tool in the scientific reasoning process during a set of learning activities. These activities were published in an online learning envi-ronment to foster collaborative learning. Pupils mapped their discussions in pairs, shared maps via the online forum and in plenary discussions, and wrote essays based on their dialogue maps. This study draws on these multiple data sources: pupils’ maps in Compendium, writings in science and reflective comments about the uses of mapping for writing. Our analysis highlights the diversity of ways, both successful and unsuccessful, in which dialogue mapping was used by these young teenagers
Mechanical Control of Spin States in Spin-1 Molecules and the Underscreened Kondo Effect
The ability to make electrical contact to single molecules creates
opportunities to examine fundamental processes governing electron flow on the
smallest possible length scales. We report experiments in which we controllably
stretch individual cobalt complexes having spin S = 1, while simultaneously
measuring current flow through the molecule. The molecule's spin states and
magnetic anisotropy were manipulated in the absence of a magnetic field by
modification of the molecular symmetry. This control enabled quantitative
studies of the underscreened Kondo effect, in which conduction electrons only
partially compensate the molecular spin. Our findings demonstrate a mechanism
of spin control in single-molecule devices and establish that they can serve as
model systems for making precision tests of correlated-electron theories.Comment: main text: 5 pages, 4 figures; supporting information attached; to
appear in Science
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